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\title{\huge \bf Cinquefoil \footnote{This file is from the 3D-XploreMath project. \hfil\break Please see http://vmm.math.uci.edu/3D-XplorMath/index.html}}
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\LARGE

Parametric Formulas for the  Cinquefoil Knot:
\begin{eqnarray*}
		P.x &:=& \cos(t)(2-\cos(2\ t/(2 \  aa + 1))); \\
		P.y &:=& \sin(t)\ (2-\cos(2\ t/(2 \  aa + 1))); \\
		P.z &:=& -\sin(2\ t/(2 \  aa + 1)); \\
\end{eqnarray*}

The choice $aa=1$ gives the Trefoil knot, $aa = 2$ the Cinquefoil, and 
in general $aa = k$ gives the (2k+1)-foil knot (the program 
rounds aa before using it). The parameter range for $t$ 
should be 0 to $(4 \ k + 2)\ \pi$.  If you change aa in the 
Set Parameters... dialog, then these values of tMin  and 
tMax are set also, but you can change them later in the 
Set t,u,v Ranges... dialog.

A nice animation of the Cinquefoil knot can be obtained
by first choosing Show as Tube from the Action menu,
Stereo Vision from the View menu, and then Filmstrip
Animation followed by Rotate from the Animation menu. 

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